4PM1/01 Jun 2023, Question 3: Solving Equations by Graphical Methods
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 5 marks
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The question, in short
Using the given graph of y = x/2 + 4/x², add a suitable straight line to estimate the roots of 3x³ − 12x² + 8 = 0 for 0.8 < x < 7, giving each to one decimal place.
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Solution · 5 marks
- 13x³ − 12x² + 8 = 0; divide by 2x²: 3x/2 − 6 + 4/x² = 0
- 2So x/2 + 4/x² = 6 − x
- 3Draw the line y = 6 − x on the grid
- 4It meets the curve at x ≈ 0.9 and x ≈ 3.8
Answerx = 0.9 and x = 3.8
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